In the figure shown, a ball without sliding on a horizontal, surface. It ascends a curved track up to height `h` returns. The value of h is `h_(1)` for sufficiently rough curved track to avoid sliding and is `h_(2)` for smooth curved track then

Options

A. `h_(1)=h_(2)`
B. `h_(1)lt h_(2)`
C. `h_(1)gth_(2)`
D. `h_(2)=2h_(1)`

Answer

C

Explanation

If the track is smooth (case A), only transitional kinetic energy changes to the gravitational potential energy.
But, if the track is rough (Case B), both translational and rotational kinetic energy changes to potential energy. Therefore, potential energy (=mgh) will be more in case B than in case A hence `h_(1) gt h_(2)`
hence (3)